Investigation of the field theories for topological insulators and unified models of elementary particles

• Project/Area Number: 24540247
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Particle/Nuclear/Cosmic ray/Astro physics
• Research Institution: Ibaraki University
• Principal Investigator: Takanori Fujiwara 茨城大学, 理学部, 教授 (50183596)
• Project Period (FY): 2012-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000); Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
• Keywords: 場の理論 / トポロジカル絶縁体 / 量子異常 / 格子模型 / 位相不変量 / 指数定理 / エネルギー固有値 / 一様磁場 / ゲージ理論 / 格子ゲージ理論 / Dirac演算子 / バルクエッジ対応 / モノポール / インスタントン / Dirac方程式 / field theory / topological insulator / anomaly / index theorem / gauge field / effective theroy / magnetized torus / theta function

Outline of Final Research Achievements

Topological insulators have a gap that is stable under continuous deformation of parameters. It is known that a bulk topological insulator is characterized by a topological invariant called such as the Chern number. In finite topological insulators there appear characteristic edge states at the surface and the gap closes. To get insight into the phenomena and seek for possible application to unified theories of elementary particles we have introduced periodic lattice models of topological insulators and investigated the response of energy epectra with applied electromagnetic fields. To compare field theoretical approaches we have also studied the eigenvalue problem for Dirac operators on uniformly magnetized tori in arbitary dimensions and give a construction of exact zero-mode solutions.

Research Products

• [Journal Article] Streda formula for the Hofstadter-Wilson-Dirac model in two and four dimensions (2016)
  • Author(s): T. Fukui and T. Fujiwara
  • Journal Title: J. Phys. Soc. Jpn. Volume: 85 Issue: 12 Pages: 124709-124709
  • DOI: 10.7566/jpsj.85.124709
  • NAID: 130006710554
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Generalized index theorem for topological superconductors with Yang-Mills-Higgs couplings (2012)
  • Author(s): Takanori Fujiwara, Takahiro Fukui
  • Journal Title: Phys. Rev. D Volume: 85 Issue: 12 Pages: 125034-125034
  • DOI: 10.1103/physrevd.85.125034
  • Peer Reviewed
• [Journal Article] Bulk-Edge Correspondence for Chern Topological Phases: A Viewpoint from a Generalized Index Theorem (2012)
  • Author(s): Takahiro Fukui, Ken Shiozaki, Takanori Fujiwara, and Satoshi Fujimoto
  • Journal Title: Journal of the Physical Society of Japan Volume: 81 Issue: 11 Pages: 114602-114602
  • DOI: 10.1143/jpsj.81.114602
  • NAID: 210000109778
  • Peer Reviewed